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ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 6, pp. 774–796. c Pleiades Publishing, Ltd., 2007. Original Russian Text c A.A. Amosov, I.A. Goshev, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 6, pp. 760–779. PARTIAL DIFFERENTIAL EQUATIONS Global Unique Solvability of the Longitudinal Vibration Equations of the Ishlinskii Viscoelastoplastic Material A. A. Amosov and I. A. Goshev Moscow Institute of Power Engineering (State University), Moscow, Russia Received March 13, 2006 DOI: 10.1134/S0012266107060055 1. STATEMENT OF THE PROBLEMS In the present paper, we prove the existence and uniqueness of global generalized solutions of initial-boundary value problems for the system of quasilinear operator-differential equations D e = Du in Q, (1.1) D u = Dσ + g [x ]in Q, (1.2) t e ν[η] σ = Du + σ [e]+ F s ,e,μ ,η = e +1 in Q, (1.3) el D x = u in Q (1.4) t e describing longitudinal vibrations of the Ishlinskii viscoelastoplastic material. The unknown vector function z(x, t)= (e(x, t),u(x, t),σ(x, t),x (x, t)) is defined on Q = Q =Ω × (0,T ), where Ω = (0,X). Here we have used the notation D = ∂/∂t, T t D =
Differential Equations – Springer Journals
Published: Jul 23, 2007
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